652 BELL SYSTEM TECHNICAL JOURNAL 



electrons in the same orbit have different values for their fourth quan- 

 tum number. We shall use the term "quantum state" to signify the 

 permitted behavior corresponding to specified values for the four 

 quantum numbers. In this language, Pauli's principle asserts simply 

 that no two electrons in a given atom can be simultaneously in the 

 same quantum state; that is, Pauli's principle is a quantum mechanical 

 analogue of the classical principle that two bodies cannot occupy the 

 same place at the same time. The two ideas — first that the motions 

 of the electrons are quantized so that only certain quantum states are 

 allowed, and second that in an atom only one electron can occupy a 

 given quantum state — form the basis of all quantum mechanical 

 thinking. We shall make use of them continually in the following 

 discussion. We shall use them, however, not in connection with the 

 orbits of Bohr but instead with the wave functions of Schroedinger. 



The Bohr theory can be applied only with difficulty to any atom 

 but hydrogen. The difficulty lies in determining the motions of the 

 electrons in the complex interacting fields of the electrons and the 

 nucleus. This problem is even more difficult in the case of a solid 

 where there are many atoms, and it would seem hopeless to try to find 

 out why the electronic orbits in insulating crystals such as rock salt 

 or diamond do not permit electrons to move through the crystal and 

 carry a current, while the orbits in metals do. Indeed not only does 

 the Bohr theory have the foregoing disadvantage but it is probably 

 wrong. Fortunately there is a theory both sounder and easier to apply 

 embodied in the "wave equation of Schroedinger." 



One feature, probably not sufficiently stressed, about Schroedinger's 

 equation is its relative convenience. The word "relative" must be 

 used here because it is usually very laborious to obtain solutions for the 

 equation and only in the simplest cases can we obtain exact solutions. 

 Compared to the classical equations and the equations of Bohr, how- 

 ever, it is convenient. Quite satisfactory approximate solutions can 

 be obtained for Schroedinger's equation even for the complex case of 

 solids, where it would be prohibitively difficult to obtain as good 

 solutions for the classical and Bohr equations. 



Electrons in Atoms 

 According to the Schroedinger theory, a diff"erential equation can 

 be written down for any system consisting of electrons and atomic 

 nuclei. This equation contains an unknown wave function and an 

 unknown energy and the instructions of the theory are to solve the 

 equation for the unknown quantities. Furthermore, the wave func- 

 tion must satisfy a certain mathematical requirement which embodies 



